All right, let's start with writing down everything that we know. We know the velocity me is 4.5 times 10 to the sixth. That's in meters per second. They are given the force produced by the magnetic field so abbreviate that have sabih that is equal to 8.0 times 10 to the minus 14. Now our force, as usual, is in Newton's. So were given that this is a traveling proton going at the speed. It's another thing will want. A note is the charge of a proton is 1.6 times, then B minus 19th power that is in cool unit of charge. It is the charge of a proton, so electrons and protons share the same charge. Point of note. Electrons Air Just opposite Lee directed opposite Lee charged. Now the equation we're gonna want to use to find the magnetic field it's given by B is equal to divided by the charge multiplied by he sign of the angle between the velocity and the force. They were given in this problem that the velocity is traveling east and the force is directed south. So it's right. So we have our velocity and Of course, these are 90 degrees to each other. So we have sign of 90 degrees or sign of pile for two, which is equal to one. So we don't need to keep that in this equation. No, this is a straight up plug and chug. Um, we have everything we need to calculate it, but we need to find out the direction so you can find this from using the right hand rule. If you hold your right hand palm upwards out in front of you, point you some out to the side, point your pointer finger directly forward, and then your middle finger will point up in the direction your palm is facing. They should all be at right angles to each other all perpendicular. So your pointer finger is the direction of the Byfield. Your thumb is in the direction of the velocity, and your middle finger will be the force. So if we or intake orientate our right hand in the direction we're given. So we have velocity to the east or to the right. Then we had the forces south. So you feel you'll have the bend your right hand around your middle finger or your palm is facing downwards and your thumb is pointing to the right. That should leave your pointer finger facing directly at your your faith or your chest, depending on how you're able to angle your hand for that. But for this diagram, this is a three dimensional. Um, this is a three dimensional problem, but we only have two dimensions here, So this is going to be coming out of the page. Um, which is represented by a circle with a DOT, whereas into the page is represented by an ax inside of the city. This is out of the pages in. Okay, so now we have direction squared away. Weaken, calculate this out. Plugging in all of this gives you that be, is what we're solving for. The magnetic field is equal to 0.1 one. So we have a number. Let's make sure it's what we want by double checking with their units. So F is in units of Newton's que is in units of cools See And now he is in units meters per second. So it's cool moms times meter for a second. If you wanted to help you see the next appear low but easier. You can put the Coolum in the numerator here just time. Cool, sometimes meter divided by second. So but want to do is move this second up to the numerator. We can do that. You can see it a little easier if you just read it in seconds over one to move it up. You just flip it. So this isn't this denominator here. So we we flip it so it would be seconds over one multiplied by that. So what we're left with is Newton time second over, cooling times, meter for meter times. Cool. Which is the definition of the Tesla, which is our units for magnetic field. The abbreviated as a t. You know, we have a final answer be is equal to zero point point 11 test now to find what what happened with an electron? As I said earlier, electron in protons have the same charge. That wouldn't affect any of the numbers. Uh, for the proton, it's directed out of the page, as we discovered with the right hand roll with a negative charge. You do that opposite of what you find with her again rule to make things even more confusing. So we found that this points out of the page with an electron. It's just imagine your middle finger pointing in the opposite direction is actually pointing, So we'll be pointing into the page, which is the opposite of what we found for the proton. So for part B, we have an electron that would be in the page, same number, and there you have it.